The system performance improvement in dispersion managed (DM) links combined with optical phase conjugator (OPC) for compensating for optical signal distortion due to group velocity dispersion and nonlinear fiber effects has been reported. However, in DM link combined OPC, the equalities of the lengths of singlemode fibers (SMFs), the length of dispersion compensating fibers (DCFs), the dispersion coefficient of DCF, and the residual dispersion per span (RDPS) with respect to an OPC restrict a flexible link configuration. Thus, in this paper, we propose a flexible optical link configuration with inequalities of link parameters, the socalled “pseudosymmetric configuration.” Simulation results show that, in the restricted RDPS range of 450 ps/nm to 800 ps/nm, the improvement in the system performance of the proposed pseudosymmetrically configured optical links is better than that of the asymmetrically configured optical links. Consequently, we confirmed that the proposed pseudosymmetric configuration is effective and useful for implementing a reconfigurable longhaul wavelengthdivision multiplexing (WDM) network.
I. INTRODUCTION
Groupvelocity dispersion (GVD) and nonlinearity of optical fibers are two major factors limiting the high bit rate and length (BL) product in optical communication systems
[1
,
2]
. Dispersion management (DM) is a very effective technology in ultrafast highbitrate optical communication lines, if nonlinearity is neglected. A dispersionmanaged optical fiber is designed to achieve low (or even zero) pathaveraged GVD by using a periodic chain of spans, that is, by inserting the dispersion compensating fiber (DCF) with anomalous GVD into a singlemode fiber (SMF) with normal GVD
[3

5]
.
Besides DM technology, optical phase conjugation is an alternative approach to mitigate the GVD effect and the nonlinearity effects; in particular, this approach is more effective in compensating for the distorted optical signals due to the interaction of the GVD and the selfphase modulation (SPM) among nonlinearities
[6

8]
. The compensation for signal impairment in this technique is theoretically possible through the use of an optical phase conjugator (OPC) in the middle of the entire transmission line. The phaseconjugated signal generated by the OPC carries the same data as the original signal, but the sig¬nal spectrum is inverted to compensate for the optical pulse distortion.
However, DM and optical phase conjugation have certain limitations, such as less compensation for the optical signal distortion due to nonlinear effects in only DM, and the practical difficulty of the symmetry of the dispersion distribution and the strength of the optical power distribution along the fiber with respect to the position of the OPC
[8]
. Fortunately, a combination of DM and OPC has been recently proposed for overcoming these problems
[9

12]
.
In the optical link with a combination of DM and optical phase conjugation, the compensation for the signal distortions depends upon the equalities of the fiber span parameters, such as the SMF length, the DCF length, the dispersion coefficient of DCF, and the residual dispersion per span (RDPS), between the former halftransmission section (before OPC) and the latter halftransmission section (after OPC)
[3

5
,
13]
. In particular, in the case of a wavelengthdivision multiplexing (WDM) system, it is difficult to find the best link condition determined by the abovementioned parameters. This is attributed to the fact that if perfect dispersion compensation is accomplished for a particular channel of the WDM system, other wavelength channels may encounter different amounts of cumulative dispersion proportional to their wavelength separations from the zeroaveragedispersion wavelength channel
[14
,
15]
.
Thus far, most works have focused only on either the DM techniques or the combined DM and OPC techniques for uniformly deployed optical links by equalizing the fiber span parameters in the former half section with those in the latter half section. This uniform link configuration makes the optical link design simple, but the implementation of a reconfigurable optical link is very difficult. To the best of the author’s knowledge, the performance assessments of a DM and OPCcombined link with the fiber span parameters in both half sections are not equal to each other and are yet to be reported.
Therefore, in this paper, we propose a new optical link scheme having the capability to flexibly implement optical link configurations. The SMF lengths of 80 km and 112 km are used in the proposed optical link, but the total lengths of the former half section and of the latter half section are the same. Therefore, we call this link scheme “pseudosymmetric configuration,” wherein the SMF lengths are uniform for all fiber spans and the total lengths of both half sections are consistent in a “symmetric configuration.”
II. WDM TRANSMISSION MODELING AND NUMERICAL ASSESSMENT METHOD
The optical transmission link shown in
Fig. 1
consists of
m
+
n
fiber spans, where
m
and
n
denote the number of fiber spans in the former half section and the latter half section, respectively. However, the total transmission length of SMF, i.e., the sum of all SMF lengths is assumed to be 1120 km, irrespective of the link configurations. In the symmetric configuration,
m
=
n
= 7 and
l
_{SMF}
= 80 km for all the fiber spans.
Basic configuration of an optical link for transmitting 24channel wavelengthdivision multiplexing (WDM). EDFA: erbium doped fiber amplifier, SMF: singlemode fiber, DCF: dispersion compensating fiber, OPC: optical phase conjugator, HNLDSF: highly nonlinear dispersionshifted fiber, CC: concentrated compensation
It is assumed to be
m
≠
n
for the asymmetric configuration and the pseudosymmetric configuration. However, these two configurations are separated from each other by the total length of each half section. That is, in case of the asymmetric configuration, the half section’s total length is different from each other (i.e., 640 km and 480 km). On the other hand, the total length of the half section is the same for both sections in the pseudosymmetric configuration (i.e., 560 km). In both the configurations, the two deployment types are classified by selecting
m
,
n
, the length of the SMF, and the dispersion coefficient of the DCF, as summarized in
Table 1
.
l_{SMF}: singlemode fiber length, D_{DCF}: dispersion coefficient of dispersion compensating fiber.
The fiber parameters, except the SMF length (
l
_{SMF}
) and the dispersion coefficient of DCF (
D
_{DCF}
), in all the link configurations are fixed as follows: attenuation coefficient of SMF
α_{SMF}
= 0.2 dB/km, dispersion coefficient of SMF
D_{SMF}
= 17 ps/nm/km, nonlinear coefficient of SMF
γ_{SMF}
= 1.35 W
^{1}
km
^{1}
at 1550 nm, attenuation coefficient of DCF
α_{DCF}
= 0.6 dB/km, and nonlinear coefficient of DCF
γ_{DCF}
= 5.06 W
^{1}
km
^{1}
at 1550 nm.
RDPSs of all fiber spans, except the first and the last fiber spans, are varied from 0 ps/nm to 1350 ps/nm (50 ps/nm intervals) or 0 ps/nm to 1330 ps/nm (70 ps/nm intervals) by controlling
l
_{DCF}
, i.e., the DCF lengths according to ((
D_{SMF}
∙
l
_{SMF}
) –
RDPS
)/
D
_{DCF}
 in the configurations including
D_{DCF}
= –100 ps/nm/km or –140 ps/nm/km. These two RDPS intervals correspond with Δ
l
_{DCF}
= 0.1 km.
Because most fiber spans have arbitrary RDPS, the net residual dispersion (NRD) of each half section is not zero, but very large, except for RDPS = 0 ps/nm. Thus, we need to control the NRD of each half section by using the arbitrary span in order to obtain the optimal value for good compensation. The DCF lengths of the first fiber span and the last fiber span, i.e.,
l
_{pre }
and
l
_{post}
, are used for determining the NRD of the former half section and the latter half section, respectively.
In this paper, the optical link configurations are designed on the basis of the following concepts. 1) The precompensation (i.e., DCF + SMF) in the former half section and the postcompensation (i.e., SMF + DCF) in the latter half section are considered for an effective symmetric distribution of local dispersion with respect to OPC. 2) The NRD of the entire transmission link is determined through two concentrated places as follows: first, the entire NRD is controlled by only
l
_{pre}
, and simultaneously, the NRD of the latter half section is set to be 0 ps/nm (i.e., the complete compensation of the latter half section) by setting the fixed
l
_{post}
, which depends on
n
and the RDPS values. This NRD control scheme is called preconcentrated compensation (or preCC). Second, the entire NRD is controlled by only
l
_{post}
, and simultaneously, the complete compensation of the former half section is accomplished by setting the fixed
l
_{pre}
; this NRD control scheme is called postconcentrated compensation (postCC).
The transmitter (Tx) for the 24channel WDM shown in
Fig. 1
is assumed to be a distributed feedback laser diode (DFBLD). The center wavelengths of the DFBLDs are assumed to be 1550–1568.4 nm (0.8 nm interval, i.e., 100 GHz interval) on the basis of ITUT recommendation G.694.1. DFBLDs are externally modulated by an independent 40Gbps 127 (=2
^{7}
– 1)pseudorandombit sequence. The modulation formats from the external optical modulators are assumed to be returntozero (RZ), while the output electric field of the RZ format is assumed to be a secondorder superGaussian pulse with a 10dB extinction ratio and 0.5 duty cycle, and is chirp free.
The nonlinear medium of the midway OPC illustrated in
Fig. 1
is assumed to be the highly nonlinear dispersionshifted fiber (HNLDSF). The parameters of the OPC are as follows: loss of HNLDSF
α
_{0}
= 0.61 dB/km, nonlinear coefficient of HNLDSF
γ
_{0}
= 20.4 W
^{1}
km
^{1}
, length of HNLDSF
z
_{0}
= 0.75 km, zero dispersion wavelength of HNLDSF
λ
_{0}
= 1550 nm, dispersion slope
dD
_{0}
/
dλ
= 0.032 ps/nm
^{2}
/km, pump light power
P_{p}
= 18.5 dBm, and pump light wavelength
λ
_{p}
= 1549.75 nm.
The optical signals propagating through the former half section are converted to the conjugated signals with wavelengths of 1549.5–1528.5 nm by the midway OPC. The 3dB bandwidth of the conversion efficiency is calculated to be almost 48 nm (1526–1574 nm) from the previously mentioned OPC parameters. Thus, all the signal wavelengths and the conjugated wavelengths belong within the 3dB bandwidth of the conversion efficiency.
The receiver (Rx) consists of the preamplifier of the EDFA with a 5dB noise figure, an optical filter of 1nm bandwidth, PIN diode, pulse shaping filter (Butterworth filter), and the decision circuit. The receiver bandwidth is assumed to be 0.65 times the bit rate
[16]
.
The propagation of a signal in a lossy, dispersive, and nonlinear medium can be expressed by the nonlinear Schrödinger equation assuming a slowly varying envelope approximation. The numerical approach of (1) is completed by using the splitstep Fourier (SSF) method
[17]
.
The eyeopening penalty (EOP) is used for assessing the system performance of the receiving WDM signals in this work, as follows:
where
EO_{rec}
and
EO_{btb}
denote the eye opening (EO) of the receiving optical pulse and the EO of the input optical pulse, respectively. EO is defined as 2
P_{av}
/(
P_{1,min}
–
P_{0,max}
), where
P_{av}
represents the averaged power of the optical signals, and
P_{1,min}
and
P_{0,max}
denote the minimum power of the optical pulse “1” and the maximum power of the optical pulse “0,” respectively.
III. SIMULATION AND DISCUSSIONS
Fig. 2
(a) and (b) show the EOPs of the worst channel among the 24 WDM channels as a function of RDPSs at several NRDs in the proposed pseudosymmetric link configurations of type 1 and type 2, respectively. The results shown in
Fig. 3
(a) are obtained when the launch power is –3 dBm and the NRDs are controlled by preCC. Further, the results shown in
Fig. 3
(b) are obtained when the launch power is –5 dBm and the NRDs are controlled by postCC.
EOP of the worst channel versus RDPS at several NRD values in the optical link of the pseudosymmetrical configurations: (a) type1 link of NRD controlled by preCC with the launch power of –3 dBm and (b) type2 link of NRD controlled by postCC with the launch power of –5 dBm. EOP: eyeopening penalty, RDPS: residual dispersion per span, NRD: net residual dispersion, CC:
EOP of the worst channel as a function of RDPS in the links with the optimal NRD controlled by preCC in (b), and controlled by postCC in (a) and (c), where the launch powers are –1 dBm (a), 3 dBm (b), and 7 dBm (c). EOP: eyeopening penalty, RDPS: residual dispersion per span, NRD: net residual dispersion, CC:
In both cases, we confirmed that the EOP characteristics over the entire RDPS range when NRD = 14 ps/nm or –14 ps/nm are superior to those for other NRD values. These two NRD values correspond to a 0.1 km or –0.1 km displacement from the positions of the first DCF or the last DCF for NRD = 0 ps/nm. That is, the optimal NRD values are obtained to make the lengths of the first DCF or the last DCF shorter or longer by 0.1 km as compared to the lengths obtained when NRD = 0 ps/nm. The optimal NRD values in the rest link configurations are obtained and are the same as the results shown in
Fig. 2
. That is, the optimal NRD values are 8 (or –8) ps/nm and 10 (or –10) ps/nm in the link configurations with
D
_{DCF}
= –80 ps/nm/km and –100 ps/nm/ km, respectively.
Fig. 3
shows the EOPs of the worst channel as a function of the RDPS values at several launch powers (i.e., –1, 3, and 7 dBm) in five optical link configurations with the optimal NRD, which was obtained using the same method as that used for obtaining the results shown in
Fig. 2
. We first confirmed that the best link configuration is symmetric because the EOPs over the entire RDPS range are smaller than those in the case of the other configurations, which is irrelevant for the considered launch powers. This result can be attributed to the fact that the symmetric configuration is the best stable deployment of fibers.
However, the most significant result shown in
Fig. 3
is that the improvement in the EOP characteristics in the pseudosymmetric configurations is better than that in the asymmetric configurations, if the RDPSs are restricted to 500–800 ps/nm. The results shown in
Fig. 3
imply that even though the compensation in the case of the pseudosymmetric configurations of the optical fiber parameters is less effective than that in the case of a conventionally symmetric configuration. Further, a flexible link implementation using the different lengths of the SMF and the different coefficients of the DCF with respect to OPC is possible within the restricted range of RDPS.
Another significant result shown in
Fig. 3
is that there are no significant differences between the EOPs in all the link configurations, if the RDPS between the adjacent fiber spans is set to be very large (i.e., 1320 ps/nm or 1330 ps/nm). This result may be attributed to the fact that, in optical links with large RDPSs, the WDM pulse widths expand significantly, and thus, the peak powers are drastically suppressed, which in turn mitigate the nonlinearity effects. Further, this phenomenon is not affected by the link configurations and the launch power.
In fiber communication systems, 1dB EOP is used as the system performance criterion, which is equivalent to the pulse broadening (the ratio of the received pulse RMS width to the initial pulse RMS width) of 1.25 and corresponds to a bit error rate (BER) of 10
^{–12}
[18]
.
Fig. 4
illustrates the worst channel’s effective NRD ranges as a function of RDPS (in other words, the contours of RDPS versus NRD), which results in EOPs of less than 1 dB, in two types of asymmetrically configured and two types of pseudosymmetrically configured optical links transmitting a launch power of 7 dBm. By using the results shown in
Fig. 4
, we can obtain an EOP of less than 1 dB for the arbitrary RDPS, if the NRD within the contours is selected.
Contours of RDPS versus NRD for the launch power of 7 dBm: (a) asymmetric type1, (b) asymmetric type2, (c) pseudosymmetric type1, and (d) pseudosymmetric type2 configurations. RDPS: residual dispersion per span, NRD: net residual dispersion.
We first confirmed that the effective NRD ranges in two types of pseudosymmetric configurations are superior to those in two types of asymmetric configurations, as the effective NRD ranges appear in various RDPSs and these inner areas of the contours are wider. Simultaneously, we confirmed that, in RDPSs ranging from 450 ps/nm to 800 ps/nm, there were no effective NRD ranges in both types of asymmetrically configured optical links. On the other hand, although the effective NRD ranges are narrow, these are presented in both types of pseudosymmetrically configured optical links. Of course, these results are expected on the basis of the results shown in
Fig. 3
.
Fig. 5
illustrates the worst channel’s effective NRD ranges as a function of the launch power in five link configurations with RDPS = 560 ps/nm and NRDs controlled by postCC. As one might predict from the previous results, the improvement in the effective NRD ranges over a wide range of launch power in both types of pseudosymmetrically configured optical links is better than that in asymmetrically configured optical links, but the aspects in the case of small RDPSs and large RDPSs change, although these results are not shown graphically.
Effective net residual dispersion (NRD) as a function of the launch power in the case of RDPS = 560 ps/nm and postCC. RDPS: residual dispersion per span, CC: concentrated compensation.
We need to use other quantitative factors for a comparison of the effective NRD ranges depending upon the launch power in every link configuration. Thus, the contour area obtained from the results shown in
Fig. 5
is used as the quantitative factor. We defined the contour area as a “product of the NRD and the (launch) power,” and this is plotted in
Fig. 6
.
Product of net residual dispersion (NRD) and launch power. RDPS: residual dispersion per span, CC: concentrated compensation.
We first confirmed that better improvement in the compensation effects is achieved by using postCC than by using preCC in four link configurations for all the considered RDPS values, except the pseudosymmetric type2 configuration. We also confirmed that, as illustrated by the previous results, if the RDPS is selected to be large (1320 ps/nm or 1330 ps/nm, as in
Fig. 6
), the differences in compensation between optical link configurations are not large.
From the viewpoint of the product of the NRD and the power, a significant result shown in
Fig. 6
is that the effects of the proposed pseudosymmetrical configurations for the flexible implementation of optical links is greater in an optical link with a medium RDPS (i.e., 560 ps/nm in
Fig. 6
) than with a large RDPS.
IV. CONCLUSIONS
The simulations described in this paper were aimed at investigating the implementation possibility of the flexible optical links by using the pseudosymmetric configurations of the SMF lengths and the coefficients of DCF in the optical links with DM and the midway OPC. We first confirmed that the proposed pseudosymmetrical distributions of the fiber spans are effective for implementing a flexible optical link in the RDPS ranges of 450 ps/nm to 800 ps/nm, because the improvement in system performance in these configurations is better than that in asymmetrically configured optical links.
We also confirmed that a large RDPS is required to obtain a system performance that is less affected by the optical link configurations. Further, we confirmed that the best NRD control method for obtaining improved system performance is postCC and not preCC, irrespective of the RDPSs and the optical link configurations.
BIO
SeongReal Lee
received the B.S., M.S., and Ph.D. degrees in telecommunication and information engineering from Hankuk Aviation University, Korea in 1990, 1992, and 2002, respectively. He is currently an associate professor of the Department of Marine Information and Communication Engineering at Mokpo National Maritime University. His research interests include optical WDM systems, optical soliton systems, and optical nonlinear effects.
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